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The volume of a cube is 125 cm³ - OCR - GCSE Maths - Question 12 - 2019 - Paper 1

Question 12

The volume of a cube is 125 cm³. Calculate the total surface area of the cube. Give the units of your answer.

Worked Solution & Example Answer:The volume of a cube is 125 cm³ - OCR - GCSE Maths - Question 12 - 2019 - Paper 1

Step 1

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Answer

The volume of a cube is given by the formula:

$V = s^3$

where $s$ is the length of a side. We know the volume, $V = 125 \text{ cm}^3$ . To find $s$ , we take the cube root:

$s = \sqrt[3]{125} = 5 \text{ cm}$

Step 2

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Answer

The total surface area (SA) of a cube is given by the formula:

$SA = 6s^2$

Substituting the value of $s$ we calculated:

$SA = 6(5 \text{ cm})^2 = 6 \times 25 \text{ cm}^2 = 150 \text{ cm}^2$

Step 3

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Answer

The units of the total surface area are square centimeters (cm²).

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